\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{Theoretic quantum Information entropies for the generalized hyperbolic
potential}



\author[1]{Akpan Ikot}%
\author[1]{Gaotsiwe Joel Rampho}%
\author[2,3]{Precious Amadi }%
\author[3]{Uduakobong Okorie}%
\author[1]{Makagamathe Sithole}%
\author[1]{Mantile Lekala}%
\affil[1]{University of South Africa}%
\affil[2]{Kirchhoff-Institut für Physik}%
\affil[3]{University of Port Harcourt}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
The Shannon entropy (S) and the Fisher Information (I) entropies are
investigated for a generalized hyperbolic potential in position and
momentum spaces. Firstly, the Schrodinger equation is solved exactly
using the Nikiforov-Uvarov-Functional Analysis (NUFA) method to obtain
the energy spectra and the corresponding wave function. By Fourier
transforming the position space wave function, the corresponding
momentum wave function was obtained for the low lying states
corresponding to the ground and first excited state. The positions and
momentum Shannon entropy and Fisher Information entropies were
calculated numerically. Finally, the Bialynicki-Birula and Mycielski
(BBM) and the Stam-Cramer-Rao inequalities for the Shannon entropy and
Fisher Information entropies respectively were tested and was found to
be satisfied for all cases considered%
\end{abstract}%



\sloppy


\textbf{Hosted file}

\verb`generalized hyperbolic potential.doc`  available at \url{https://authorea.com/users/291200/articles/449293-theoretic-quantum-information-entropies-for-the-generalized-hyperbolic-potential}

\selectlanguage{english}
\FloatBarrier
\end{document}

